Question

solve the following quadratic equation:x/x+1 + x+1/x =5/2​

Answer 1

Step-by-step explanation:

◆let x/x+1 be y.

y+1/y=5/2

y^2+1=5/2y

2y^2+2=5y

2y^2-5y+2=0

2y^2-4y-y+2=0

2y(y-2)-1(y-2)=0

(2y-1)(y-2)=0

y=1/2,y=2

on putting y=1/2,

●x/x+1=1/2

●2x=x+1

●x=1

on putting y=2,

●x/x+1=2

●x=2x+2

●x=-2